Longtime lurker, first time poster. My local pub, that I used to frequent before the pandemic hit, has a dice game. $1 to play, which goes in to the pot. You roll 5 standard 6 sided dice. A three of a kind of any number gets you a free roll. Four a kind of any number gets you $100 from the pot. Five of a kind gets you the whole pot, minus 15% tip to the bartender(s) on duty at that particular time. I someone willing to do a statistical analysis of the game here. such as house edge, break even, etc? My statistics background is in clinical trials and medical studies and experiments, and not in gambling at all. Thanks for your assistance.

Gene

Is that allowed, so you can hold a pair, and reroll the other 3 dice?

You say a 3 of a kind gets a "free roll".

Does that mean you roll all 5 dice again?

Also, is any money added to the pot after it hits, or does it start from zero? What happens when someone rolls a four of a kind with less than $100 in the pot (think multiple hits in short succession)?

Quote:GenoDRPhHello All,

Longtime lurker, first time poster. My local pub, that I used to frequent before the pandemic hit, has a dice game. $1 to play, which goes in to the pot. You roll 5 standard 6 sided dice. A three of a kind of any number gets you a free roll. Four a kind of any number gets you $100 from the pot. Five of a kind gets you the whole pot, minus 15% tip to the bartender(s) on duty at that particular time. I someone willing to do a statistical analysis of the game here. such as house edge, break even, etc? My statistics background is in clinical trials and medical studies and experiments, and not in gambling at all. Thanks for your assistance.

Gene

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Welcome to the forum! It's always good to take a peek at the forum rules: Forum Rules.

The analysis you are asking for is straightforward and relatively easy. I'm busy and can't do it right now, but I'm sure someone will step up shortly.

Gene

The actual number is probably lower, and I'm happy to hear why.

Quote:DieterAssuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.

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It’s lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.

Quote:unJonQuote:DieterAssuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.

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It’s lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.

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... and as soon as someone hits the 4oK for $100, the pot shrinks, making the game undesirable.

Lots of fun math here for someone smarter than me to grind on.

Quote:DieterQuote:unJonQuote:DieterAssuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.

link to original post

It’s lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.

link to original post

... and as soon as someone hits the 4oK for $100, the pot shrinks, making the game undesirable.

Lots of fun math here for someone smarter than me to grind on.

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I don’t follow that comment. You know the prize pool when you roll. One person rolls at a time.

6^5 = 7,776 ways to roll 5 dice.

6 ways to roll 5OAK

150 ways to roll 4OAK

1,500 ways to roll 3OAK (includes full houses)

Pot is $X

6 * 0.85 * X + 150 * 100 + 1,500 * Y - (7,776 - 1,500 - 150 - 6) = 0

Y is recursive EV of playing the game again. Will calculate when back in front of Excel.

What am

I missing?